Calculator Inputs
Example Data Table
| Scenario | Focal Length (mm) | Pixel Size (µm) | Centroid Error (px) | Matched Stars | Catalog (arcsec) | Algorithm (arcsec) | Boresight (arcsec) | Thermal (arcsec) | Jitter (arcsec) |
|---|---|---|---|---|---|---|---|---|---|
| CubeSat baseline | 35 | 6.5 | 0.10 | 8 | 1.20 | 1.80 | 3.00 | 1.20 | 2.50 |
| LEO imaging bus | 50 | 7.0 | 0.08 | 12 | 0.70 | 1.10 | 2.40 | 0.90 | 1.80 |
| Fine pointing payload | 85 | 5.5 | 0.04 | 18 | 0.35 | 0.55 | 1.10 | 0.45 | 0.70 |
Formula Used
The calculator converts camera geometry into angular sensitivity first, then combines independent error sources by root-sum-square addition.
Plate Scale (arcsec/pixel) = 206.265 × Pixel Size (µm) ÷ Focal Length (mm)
Horizontal FOV (deg) = Sensor Width (pixels) × Plate Scale ÷ 3600
Vertical FOV (deg) = Sensor Height (pixels) × Plate Scale ÷ 3600
Single-Star Centroid Error (arcsec) = Centroid Error (pixels) × Plate Scale
Multi-Star Centroid Residual (arcsec) =
Single-Star Centroid Error ÷ √(Matched Stars)
Total Single-Axis 1σ Error (arcsec) =
√(Centroid² + Catalog² + Algorithm² + Boresight² + Thermal² + Jitter²)
Single-Axis 95% Error = 1.96 × Total 1σ
Single-Axis 3σ Error = 3.00 × Total 1σ
Radial RMS Error = √2 × Total 1σThis model assumes the listed contributors are statistically independent. That makes it suitable for early design work, requirement flowdown, and fast trade studies.
How to Use This Calculator
- Enter focal length and pixel size to define angular scale.
- Enter sensor width and height to estimate field of view.
- Enter centroiding error in pixels from image processing performance.
- Set the number of matched stars used in the attitude solution.
- Fill in catalog, algorithm, boresight, thermal, and jitter errors in arcseconds.
- Press Calculate Accuracy to display the result block above the form.
- Review the contributor chart, summary table, and export buttons for reporting.
FAQs
1. What does this calculator estimate?
It estimates star tracker attitude knowledge accuracy from optics, sensor geometry, centroiding quality, matched star count, and major error budget terms. The main output is single-axis angular error in arcseconds.
2. Why is centroiding entered in pixels?
Centroiding accuracy is usually measured relative to detector pixels. The calculator converts that pixel error into arcseconds by using plate scale, which links sensor geometry to angular measurement sensitivity.
3. Why does increasing matched stars improve accuracy?
Using more matched stars averages random centroid noise across the solution. The simplified model reduces centroid residual by dividing the single-star centroid error by the square root of the matched star count.
4. What is the difference between 1-sigma and 3-sigma?
One-sigma shows the standard deviation level for the modeled single-axis error. Three-sigma is a more conservative bound, often used when teams want margin for requirements, mission assurance, or pointing budget reviews.
5. What does boresight calibration represent?
Boresight calibration represents the angular alignment uncertainty between the tracker frame and the spacecraft or payload reference frame. Poor alignment calibration can dominate final attitude knowledge even if centroiding is excellent.
6. Is radial RMS the same as single-axis accuracy?
No. Single-axis accuracy refers to one angular axis. Radial RMS combines two orthogonal axes under an isotropic assumption, so it is larger than the single-axis one-sigma estimate.
7. Can I use this for thermal trade studies?
Yes. Change the thermal drift term while holding the other inputs fixed. That makes it easy to see how thermal control quality affects final attitude knowledge and whether tighter thermal design is justified.
8. When should I use a more detailed model?
Use a more detailed model when you need time-varying smear, lost-in-space behavior, false stars, stray light, nonlinear distortion, covariance propagation, or closed-loop spacecraft dynamics inside the pointing estimate.